After obtaining the test functions, we can perform hypothesis tests for covariance properties based on nonparametric functional data ranking.
We use a similar testing procedure to that introduced by [1]} for a univariate spatio-temporal covariance.
The key idea is to test whether two functional data sets are from the same distribution [2]}, which requires to generate reference data under the null covariance model described in Table REF . Figure REF  illustrates the entire testing procedure.
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